To introduce the effective \(t\) -\(J\) -\(K\)  model for describing the low-energy
physics of nickelates, we start from a background lattice of Ni\(^{1+}\)  3\(d_{x^2-y^2}\)  localized spins with a small number of self-doped holes and Nd-5\(d\)  conduction electrons [1]}. Similar to cuprates, one
expects an AF superexchange interaction between Ni\(^{1+}\)  spins through the
O-2\(p\)  orbitals. This is different from heavy fermion systems, where the
exchange interaction between localized spins originates from the
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediated by conduction
electrons. The motion of holes on the spin lattice should be strongly
renormalized as in the usual \(t\) -\(J\)  model. There is an additional local
Kondo interaction between local spins and conduction electrons. The total
Hamiltonian therefore contains three terms:
\(H=H_{t}+H_{J}+H_{K},\) 
